Problem: Simplify the following expression: $p = \dfrac{x^2 - 12x + 20}{x - 10} $
First factor the polynomial in the numerator. $ x^2 - 12x + 20 = (x - 10)(x - 2) $ So we can rewrite the expression as: $p = \dfrac{(x - 10)(x - 2)}{x - 10} $ We can divide the numerator and denominator by $(x - 10)$ on condition that $x \neq 10$ Therefore $p = x - 2; x \neq 10$